Non-position-aware downlink channel estimation and positioning method assisted by reconfigurable intelligent surface

Abstract

Reconfigurable intelligent surface is considered as one of the key technologies to improve the performance of the system in multiple-input multiple-output communication systems. When the system works at very high frequencies (such as terahertz), the sparsity of channel parameters becomes a significant feature. In order to effectively recover these channel parameters, we introduce an optimization method based on the atomic norm, which uses the sparsity in the angular domain to accurately estimate the channel state information. In the mixed reconfigurable intelligent surface scenario, the selection of randomly activated elements aims to reduce the cost of reconfigurable intelligent surface deployment while maintaining the performance of channel estimation and positioning. Simulation experiments show that this method can achieve super-resolution channel estimation and outperform the existing orthogonal matching pursuit method. Comparison of various performance indicators shows that the proposed method has obvious advantages. This advantage is crucial for achieving accurate positioning services in complex environments.

Description

TECHNICAL FIELD

[0001] The application relates to a non-position-aware downlink channel estimation and positioning method based on reconfigurable intelligent surface assistance and belongs to the technical field of antenna array signal processing. BACKGROUND

[0002] With the rapid progress of wireless communication technology, the sixth generation communication system has attracted extensive attention. The sixth generation aims to surpass the performance of the current fifth generation communication system by achieving higher data throughput, lower transmission latency and higher connection density to meet the needs of future communication. In order to achieve these performance indicators, the sixth generation is expected to utilize the terahertz frequency band, which is known for its wide bandwidth and the potential to provide extremely high data rates and capacity. Although the terahertz frequency band offers tremendous potential advantages, the signals in this frequency band suffer from significant path loss during propagation, which limits the range and efficiency of its practical applications. To address this challenge, multiple-input multiple-output technology is considered to improve system performance. Multiple-input multiple-output technology can effectively improve the spatial multiplexing rate of signals by deploying multiple transmit and receive antennas, thereby enhancing the spectral efficiency of the system. However, in the terahertz frequency band, even with large-scale multiple-input multiple-output technology, the system still relies heavily on line-of-sight propagation. In complex wireless environments, such as non-line-of-sight scenarios commonly found in urban landscapes, it is extremely difficult to obtain stable line-of-sight propagation paths. This dependence on line-of-sight paths exacerbates the application difficulties of terahertz communication in real-world environments.

[0003] The above problem should be considered and solved in the channel estimation and positioning of the scene based on the planar array hybrid reconfigurable intelligent surface. SUMMARY

[0004] In the scene based on the planar array hybrid reconfigurable intelligent surface, we successfully decompose the channel from the user to the base station through the reconfigurable intelligent surface into two independent sub-channels, and overcome the problems existing in the conventional hybrid reconfigurable intelligent surface. At the same time, by utilizing the baseband processing capability of the hybrid reconfigurable intelligent surface, we design the optimal phase control matrix and provide the corresponding theoretical proof. Based on this design, we also realize the three-dimensional positioning of the base station and the user with the reconfigurable intelligent surface as the coordinate origin. The technical solution of the application is:

[0005] A non-position-aware downlink channel estimation and positioning method based on reconfigurable intelligent surface assistance, characterized by comprising the following steps,

[0006] S1, according to the Saleh-Valenzuela channel model, a channel model of a user passing through a smart metasurface to a base station is constructed, and by using the baseband processing capability of a hybrid reconfigurable smart surface, the channel model of the user passing through the smart metasurface to the base station can be decomposed into two sub-channel estimation problems, which are a sub-channel between the user and the reconfigurable smart surface and a sub-channel between the reconfigurable smart surface and the base station;

[0007] S2, the channel matrix solving problem of the two sub-channels can be converted into an atomic norm minimization problem, and then a decoupled atomic norm method is used to solve each channel parameter to reduce the calculation amount;

[0008] S3, after obtaining each channel parameter, the phase control matrix of the reconfigurable smart surface that is optimal for a single user can be obtained through the incident angle information and the reflection angle information of the reconfigurable smart surface;

[0009] S4, after obtaining the two sub-channel matrices and the phase control matrix, a channel matrix of the user passing through the smart metasurface to the base station can be constructed, and then according to the obtained path gain, a single slope model can be obtained, and the three-dimensional coordinates of the user and the base station with the reconfigurable smart surface as the origin can be obtained, and then the relative position of the user and the base station can be obtained.

[0010] 2. A non-position-aware downlink channel estimation and positioning method based on reconfigurable smart surface assistance, characterized in that: in step S1, according to the Saleh-Valenzuela channel model, a channel model of a user passing through a smart metasurface to a base station is constructed, specifically, S11, we consider a hybrid reconfigurable smart surface assisted multiple-input multiple-output system, which includes a base station, a reconfigurable smart surface and multiple users, the base station and the users are respectively configured with uniform linear arrays with N B and N M array elements, and the reconfigurable smart surface is configured with a uniform planar array with N R array elements, and the spacing between the array elements of each array is half a wavelength. We assume that there is a control link between the reconfigurable smart surface and the base station, and that the direct path between the user and the base station does not exist due to being blocked.

[0011] S12, In the channel modeling, we adopt the SV channel model to describe the channel characteristics between the mobile users and the reconfigurable intelligent surface. The model takes the angle of arrival, angle of departure, and the corresponding path loss as the basic parameters. Given that our goal is to achieve channel estimation and positioning of mobile users, this model focuses on the contribution of the direct path and ignores other multipath effects. In our current research scenario, since only the direct path is considered, its corresponding time delay is zero, so the path gain can be simplified as a real number. Based on this assumption, we can derive the channel model expression between the mobile users and the reconfigurable intelligent surface as,

[0012]

[0013] where [θ M,R ] k denotes the transmit angle of the kth user, and denote the azimuth and elevation angles of the kth user incident at the reconfigurable intelligent surface, respectively, [ρ M,R ] k denotes the path loss of the kth user under the direct path, K denotes the total number of users, [H M,R ] k denotes the channel matrix between the kth user and the reconfigurable intelligent surface; for a uniform linear array with an element spacing of half the wavelength λ / 2, its array response is

[0014]

[0015] where l denotes the number of elements of the uniform linear array, so is the array response vector at the kth user, and

[0016]

[0017] for a uniform planar array with an element spacing of half the wavelength, its array response is

[0018]

[0019] where N x denotes the number of elements of a uniform planar array in the x-axis direction in the xoy plane, N y denotes the number of elements of the uniform planar array in the y-axis direction, so is the array response vector of the kth user received at the reconfigurable intelligent surface, and

[0020]

[0021] S13, similar to formula (1), the channel between the reconfigurable intelligent surface and the base station is

[0022]

[0023] wherein υ R,B denotes the receiving angle at the base station, and denote the azimuth angle and the elevation angle of the reflection at the reconfigurable intelligent surface, respectively, γ R,B denotes the path loss of the direct path between the reconfigurable intelligent surface and the base station, and and have the same definition as in the previous formula, and have the same definition as in the previous formula.

[0024] Thus, using the above formula and jointly considering the reconfigurable intelligent surface, the total channel matrix is,

[0025]

[0026] wherein is the phase control matrix of the reconfigurable intelligent surface, at this time we assume that the reconfigurable intelligent surface is composed of a series of discrete phase controllers, that is, Ω = diag(ω), wherein and a ∈ [0, 1], here we assume that the reconfigurable intelligent surface is a perfect reflection surface, that is, let a = 1.

[0027] 3. Further, in step S2, using the architecture of step S1, the channel matrix solving problem of the two sub-channels can be converted into an atomic norm minimization problem, and then the decoupled atomic norm method is used to solve each channel parameter to reduce the calculation amount, specifically,

[0028] S21, we consider uplink pilot training channel estimation, and the N M antenna elements of the user send the pilot training sequence to the reconfigurable intelligent surface at the b-th time slot as b ∈ {1, 2,..., B}, and [S b ] :,1 = [S b ] :,2 = ··· = [S b ] :,T The phase control vector of the reconfigurable intelligent surface at the b-th time slot is denoted as , and At the t-th snapshot in the b-th time slot, t ∈ {1, 2,..., T}, the M AAn element belongs to an index set As The phase of the reconfigurable intelligent surface phased matrix at the t-th snapshot in the b-th time slot on this index set is [Ω b ] i,i = 0 when For convenience of subsequent description, we set N R = M A × T here, and the advantage of this is that as long as M A element positions are selected every snapshot, then after T snapshots, we can concatenate T M A dimensional single-snapshot data in order to obtain an N R dimensional single-snapshot data, for example, F = [E1, E2, …, E T ] T , where The order of this N R dimensional single-snapshot data is chaotic compared to the order of the N R dimensional single-snapshot data under the full element array of the reconfigurable intelligent surface. Thus, the t-th snapshot data in the b-th time slot is

[0029] X bt = Ξ t H M,R [S b ] :,t +N bt

[0030] , where Each column of the matrix has at most one element equal to 1, and the rest are zero, and the number of elements equal to 1 in the matrix is M A ; Indicates independent and identically distributed additive Gaussian white noise, and obeys CN(0, σ 2 ), where σ 2 represents the variance of the noise.

[0031] Concatenate T M A dimensional single-snapshot data in order to obtain an N R dimensional single-snapshot data Thus, the received signal at the b-th time slot at the reconfigurable intelligent surface is represented as follows,

[0032]

[0033] , where , where Each row and each column of the matrix has at most one element equal to 1, and the rest are zero, and the number of elements equal to 1 in the matrix is M​A ×T=N R Ξ is an identity array if and only if the receiving array elements of the reconfigurable smart surface are sequentially selected; Represents T M A A new N is formed by concatenating independent and identically distributed additive white Gaussian noise in dimension N. R Gaussian white noise of dimension N, and because each N bt All obey CN(0,σ) 2 Therefore, N b Still obeys CN(0,σ) 2 At this time, it is ordered Therefore, the received signals of all B time slots at the first-stage reconfigurable smart surface as follows,

[0034]

[0035] S22. Now we will begin to discuss the received signal at the base station, specifically the received data in the t-th snapshot of the b-th time slot. as follows,

[0036]

[0037] in [Ω] b ] i,i =0, when hour; Let represent independent and identically distributed additive white Gaussian noise, and let CN(0,σ) be the expression. 2 ), where σ 2 Let represent the variance of the noise. Therefore, let

[0038]

[0039] Obtain the received signal when the base station is in the b-th time slot. as follows,

[0040] Y b =H R,B U b +Z b

[0041] At this time, Therefore, the received signals at the base station in the second stage total B time slots. as follows,

[0042] Y Sec =H R,B U+Z

[0043] S23. In the first stage, we need to establish the channel matrix H between the user and the reconfigurable smart surface. M,R To recover it, we first need to construct H. M,R The decoupled set of atoms is as follows.

[0044]

[0045] Therefore, we can construct an equivalent SDP optimization model. It should be noted that, due to the non-convexity of rank calculation, the following equation is a trace minimization problem obtained by substituting the trace for the rank, which is the convex relaxation mentioned earlier, where atoms... Norm convex relaxation to atoms Norms, as follows:

[0046]

[0047] Therefore, it can be further written as the following optimization problem.

[0048]

[0049] Among them κ M This is a regularization parameter used to balance signal sparsity and data fidelity. How to choose this parameter is currently unclear, but under the assumption of independent and identically distributed Gaussian noise, it is generally set to... The Toplitz matrix can be obtained by solving the above equation. and and channel matrix We can do this by... and The receiving angles of the reconfigurable smart surface are obtained by solving the problem. and the emission angle on the user side This solution algorithm can be either Root-MUSIC or ESPRIT; however, after obtaining the receive angles of the K reconfigurable smart surfaces and the transmit angles of the K user sides, we lose the correspondence between the receive angles and transmit angles. This relates to how to reconstruct the channel matrix between the reconfigurable smart surfaces and each user, and is also an unavoidable problem after decoupling. To solve this problem, we first need to... M,R After vectorization, we have:

[0050]

[0051] From the above formula, we can find that vec(H) M,R All the bases are composed of Composed of K quantities 2 There are 3 bases, and the bases are orthogonal to each other, so we can use... Construct all bases, to For the target function, we borrow the OMP algorithm to solve this problem, which can obtain the corresponding relationship between the receiving angle and the transmitting angle and their respective path loss

[0052] After obtaining the corresponding relationship between the receiving angle, the transmitting angle and the path loss, we can reconstruct the channel matrix between each user and the reconfigurable intelligent surface, where the reconstructed channel matrix of the kth user is as follows,

[0053]

[0054] In the second stage, we need to recover the channel matrix H between the base station and the reconfigurable intelligent surface by using the received signal at the base station R,B At this time, we also need to use the total channel matrix between the reconfigurable intelligent surface and all user terminals obtained from the first stage Thus we can obtain As follows,

[0055]

[0056] Further, we can obtain

[0057] If we want to recover the channel matrix H between the base station and the reconfigurable intelligent surface R,B We need to construct H R,B The decoupled atom set is as follows,

[0058]

[0059] Thus we can construct the equivalent SDP optimization model, and the same reason is as follows,

[0060]

[0061] Thus it can be further written as the following optimization problem,

[0062]

[0063] Where κ N is a regularization parameter, which is generally set to By solving the above formula, we can obtain the Toeplitz matrix and and the channel matrix We can obtain the reflection angle of the reconfigurable intelligent surface and the receiving angle of the base station by solving and The solution algorithm can be Root-MUSIC or ESPRIT algorithm; at this time, the path loss between the reconfigurable intelligent surface and the base station is obtained As follows,

[0064]

[0065] 4. Further, in step S3, after obtaining the channel parameters in step S2, the optimal phase control matrix of the reconfigurable intelligent surface for a single user can be obtained by using the incident angle information and the reflection angle information of the reconfigurable intelligent surface, specifically, S31, in the case of considering the known incident angle and reflection angle of the reconfigurable intelligent surface, the design of the phase control matrix of the reconfigurable intelligent surface becomes more convenient. Compared with other methods, this research does not require solving a complex phase control matrix optimization function. For the kth user, we can use a simplified process to obtain the optimal phase control matrix Ω * .

[0066]

[0067] 5. Further, in step S4, after obtaining the two sub-channel matrices and the phase control matrix in step S3, we can combine them to construct the channel matrix of the user through the intelligent super surface to the base station, and then according to the obtained path gain, we can obtain the three-dimensional coordinates of the user and the base station with the reconfigurable intelligent surface as the origin, and then we can obtain the relative position of the user and the base station, specifically,

[0068] S41, for distance estimation, we consider the single slope model of the path loss and distance function, and the model formula can be expressed as follows,

[0069]

[0070] where P r represents the received power, P t represents the transmitted power, K is a constant coefficient dependent on the antenna characteristics and the average channel loss, which is generally set to d r is the reference distance of the antenna, which is usually assumed to be d r = 1m, is the actual distance, is the path loss exponent, which is usually assumed to be

[0071] Therefore, the path loss can be expressed as,

[0072]

[0073] Then [ρ M,R ]k and [gamma R,B ] k Substituting into the above formula, the distance between the respective transmitting end and receiving end can be obtained respectively After successfully estimating the distance between the user and the reconfigurable intelligent surface and the distance between the reconfigurable intelligent surface and the base station, combined with the previously calculated incident angle and reflection angle of the reconfigurable intelligent surface, we can use the distance and angle information to deduce the relative positions of the base station, the reconfigurable intelligent surface and the user in the three-dimensional coordinate system through geometric relationship. Thus, the base station knows the position of the user and the distance between each other.

[0074] The beneficial effects of the present application are: we use a hybrid architecture reconfigurable intelligent surface. By splitting the channel involving the reconfigurable intelligent surface into two sub-channels for solving, and then introducing a proper phase control matrix, the total channel matrix from the user end through the reconfigurable intelligent surface to the base station can be obtained, realizing super-resolution channel estimation. In addition, we also establish a relationship model between path loss and distance, so that the base station can obtain the position information of the user. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 is a flowchart of the reconfigurable intelligent surface assisted non-position-aware channel estimation and positioning method based on the embodiments of the present application;

[0076] Figure 2 is a schematic diagram of the reconfigurable intelligent surface assisted uplink communication system in the embodiments;

[0077] Figure 3 is a schematic diagram of the construction of the reconfigurable intelligent surface in the embodiments;

[0078] Figure 4 is a schematic diagram of the pilot frame structure of the uplink in the embodiments;

[0079] Figure 5 is a schematic diagram of the incident signal and reflection signal angle of the reconfigurable intelligent surface in the embodiments;

[0080] Figure 6 is a comparison of the channel estimation performance between the user and the reconfigurable intelligent surface in the embodiments;

[0081] Figure 7 is a comparison of the channel estimation performance between the reconfigurable intelligent surface and the base station in the embodiments;

[0082] Figure 8 is a comparison of the path gain performance between the user and the reconfigurable intelligent surface and the reconfigurable intelligent surface and the base station in the embodiments, which can reflect the accuracy of distance estimation. DETAILED DESCRIPTION

[0083] The preferred embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0084] Embodiment

[0085] A non-position-aware downlink channel estimation and positioning method based on reconfigurable intelligent surface assistance, like Figure 1 , characterized in that it comprises the following steps,

[0086] S1, according to the Saleh-Valenzuela channel model, a channel model of a user passing through an intelligent super surface to a base station is constructed, like Figure 2 , using the baseband processing capability of the hybrid reconfigurable intelligent surface, the channel model of the user passing through the intelligent super surface to the base station can be decomposed into two sub-channel estimation problems, which are the sub-channel between the user and the reconfigurable intelligent surface and the sub-channel between the reconfigurable intelligent surface and the base station;

[0087] S2, the channel matrix solving problem of the two sub-channels can be converted into an atomic norm minimization problem, and then the decoupled atomic norm method is used to solve each channel parameter to reduce the calculation amount, like Figure 3 and Figure 4 ;

[0088] S3, after obtaining each channel parameter, like Figure 5 , the phase control matrix of the reconfigurable intelligent surface that is optimal for a single user can be obtained through the incident angle information and the reflection angle information of the reconfigurable intelligent surface;

[0089] S4, after obtaining the two sub-channel matrices and the phase control matrix, we can combine them to construct the channel matrix of the user passing through the intelligent super surface to the base station, then according to the obtained path gain, we can obtain the three-dimensional coordinates of the user and the base station with the reconfigurable intelligent surface as the origin, and then we can obtain the relative position of the user and the base station.

[0090] 2. A non-position-aware downlink channel estimation and positioning method based on reconfigurable intelligent surface assistance, characterized in that in step S1, according to the Saleh-Valenzuela channel model, a channel model of a user passing through an intelligent super surface to a base station is constructed, specifically, S11, we consider a hybrid reconfigurable intelligent surface assisted multiple-input multiple-output system, which contains a base station, a reconfigurable intelligent surface and multiple users, the base station and the users are respectively configured with uniform linear arrays with N B and N M array elements, while the reconfigurable intelligent surface is configured with a uniform planar array with N R array elements, and the spacing between the array elements of each array is half a wavelength. We assume that there is a control link between the reconfigurable intelligent surface and the base station, and that the direct path between the user and the base station does not exist due to being blocked.

[0091] S12、In the process of channel modeling, we adopt the SV channel model to describe the channel characteristics between the mobile user and the reconfigurable intelligent surface. This model takes the angle of arrival, angle of departure, and the corresponding path loss as the basic parameters. Given that our goal is to achieve channel estimation and positioning of mobile users, this model focuses on the contribution of the direct path and ignores other multipath effects. In our current research scenario, since only the direct path is considered, its corresponding time delay is zero, so the path gain can be simplified as a real number. Based on this assumption, we can derive the channel model expression between the mobile user and the reconfigurable intelligent surface as,

[0092]

[0093] where [θ M,R ] k represents the angle of departure of the kth user, and represent the azimuth angle and the elevation angle of the kth user incident at the reconfigurable intelligent surface, respectively, [ρ M,R ] k represents the path loss of the kth user under the direct path, K represents the total number of users, [H M,R ] k represents the channel matrix between the kth user and the reconfigurable intelligent surface; for a uniform linear array with an element spacing of half the wavelength λ / 2, its array response is

[0094]

[0095] where l represents the number of elements of the uniform linear array, so is the array response vector at the kth user, and

[0096]

[0097] For a uniform planar array with an element spacing of half the wavelength, its array response is

[0098]

[0099] where N x represents the number of elements of a uniform planar array in the x-axis direction in the xoy plane, N y represents the number of elements of the uniform planar array in the y-axis direction, so is the array response vector of the kth user received at the reconfigurable intelligent surface, and

[0100]

[0101] S13, similar to formula (1), the channel between the reconfigurable intelligent surface and the base station can be obtained as

[0102]

[0103] wherein υ R,B denotes the receiving angle at the base station, and denote the azimuth angle and the elevation angle of the reflection at the reconfigurable intelligent surface, respectively, γ R,B denotes the path loss of the direct path between the reconfigurable intelligent surface and the base station, and and have the same definition as in the previous formula, and have the same definition as in the previous formula.

[0104] Thus, using the above formula and jointly considering the reconfigurable intelligent surface, the total channel matrix is,

[0105]

[0106] wherein is the phase control matrix of the reconfigurable intelligent surface, at this time we assume that the reconfigurable intelligent surface is composed of a series of discrete phase controllers, that is, Ω = diag(ω), wherein and a e [0, 1], here we assume that the reconfigurable intelligent surface is a perfect reflection surface, that is, let a = 1.

[0107] 3. Further, in step S2, using the architecture of step S1, the channel matrix solving problem of the two sub-channels can be converted into an atomic norm minimization problem, and then the decoupled atomic norm method is used to solve each channel parameter to reduce the calculation amount, specifically,

[0108] S21, we consider the uplink pilot training channel estimation, and the N M array elements of the user send the pilot training sequence to the reconfigurable intelligent surface at the b-th time slot as b e {1, 2,..., B}, and [S b ] :,1 = [S b ] :,2 = ··· = [S b ] :,T The phase control vector of the reconfigurable intelligent surface at the b-th time slot is denoted as , and At the t-th snapshot in the b-th time slot, t e {1, 2,..., T}, the MA An element belongs to an index set If then the phase of the reconfigurable intelligent surface steering matrix at the t-th snapshot in the b-th time slot on this index set is [Ω b ] i,i = 0 when For the sake of subsequent description, we assume N R = M A × T here, and the advantage of this is that as long as M A element positions are selected at each snapshot, then after T snapshots, we can sequentially connect the T M A dimensional single-snapshot data to obtain an N R dimensional single-snapshot data, for example, F = [E1, E2,..., E T ] T , where The only difference is that the order of this N R dimensional single-snapshot data is chaotic compared with the order of the N R dimensional single-snapshot data under the full element array of the reconfigurable intelligent surface. Thus, the t-snapshot data in the b-th time slot is

[0109] X bt = Ξ t H M,R [S b ] :,t +N bt

[0110] where Each column of the matrix has at most one element equal to 1, and the number of elements equal to 1 in the matrix is M A ; represents independent and identically distributed additive white Gaussian noise, and is subject to CN(0, σ 2 ), where σ 2 represents the variance of the noise.

[0111] Connect the T M A dimensional single-snapshot data to obtain an N R dimensional single-snapshot data Thus, the received signal at the b-th time slot at the reconfigurable intelligent surface is represented as follows,

[0112]

[0113] where where ​The matrix contains only one element of value 1 in each row and column, with all other elements being zero, and the number of elements of value 1 in the matrix is ​​M. A ×T=N R Ξ is an identity array if and only if the receiving array elements of the reconfigurable smart surface are sequentially selected; Represents T M A A new N is formed by concatenating independent and identically distributed additive white Gaussian noise in dimension N. R Gaussian white noise of dimension N, and because each N bt All obey CN(0,σ) 2 Therefore, N b Still obeys CN(0,σ) 2 At this time, it is ordered Therefore, the received signals of all B time slots at the first-stage reconfigurable smart surface as follows,

[0114]

[0115] S22. Now we will begin to discuss the received signal at the base station, specifically the received data in the t-th snapshot of the b-th time slot. as follows,

[0116]

[0117] in [Ω] b ] i,i =0, when hour; Let represent independent and identically distributed additive white Gaussian noise, and let CN(0,σ) be the expression. 2 ), where σ 2 Let represent the variance of the noise. Therefore, let

[0118]

[0119] Obtain the received signal when the base station is in the b-th time slot. as follows,

[0120] Y b =H R,B U b +Z b

[0121] At this time, Therefore, the received signals at the base station in the second stage total B time slots. as follows,

[0122] Y Sec =H R,B U+Z

[0123] S23、In the first stage, we need to get the channel matrix H M,R between the users and the reconfigurable intelligent surface, for this we first construct H M,R , then decouple it into a set of atoms, as follows,

[0124]

[0125] Then we can construct the equivalent SDP optimization model, here we should point out that due to the non-convexity of the rank, the following is the trace minimization problem obtained by replacing the rank with the trace, that is, the convex relaxation mentioned earlier, which decouples the atoms with the norm into a set of atoms with the norm, as follows,

[0126]

[0127] Then it can be further written as the following optimization problem,

[0128]

[0129] where κ M is a regularization parameter used to balance the signal sparsity and data fidelity, how to choose this parameter is not very clear at present, but under the assumption of independent and identically distributed Gaussian noise, it is generally set to By solving the above equation, we can get the Toeplitz matrix and and the channel matrix We can get the receiving angle of the reconfigurable intelligent surface and the transmitting angle of the user side by solving and This solving algorithm can be Root-MUSIC or ESPRIT algorithm; but after we get the receiving angle of K reconfigurable intelligent surfaces and the transmitting angle of K user sides, we lose the correspondence between the receiving angle and the transmitting angle, which relates to how to reconstruct the channel matrix between the reconfigurable intelligent surface and each user, and is also a problem that cannot be avoided after decoupling; To solve this problem, we first need to vectorize H M,R , so we have,

[0130]

[0131] From the above equation, we can find that the entire basis of vec(H M,R ) is composed of , the number is K 2 , and the basis and the basis are mutually orthogonal, so we can use Construct all bases, to As the objective function, borrow OMP algorithm to solve the problem, in the acquisition of the corresponding relationship between the receiving angle and the transmitting angle, but also can get their respective path loss

[0132] After getting the corresponding relationship between the receiving angle, transmitting angle and path loss, we can reconstruct the channel matrix between each user and the reconfigurable intelligent surface, where the reconstructed kth user channel matrix is as follows,

[0133]

[0134] S24, in the second stage, we need to use the received signal at the base station to recover the channel matrix H between the base station and the reconfigurable intelligent surface R,B At this time, we also need to use the total channel matrix between the reconfigurable intelligent surface and all user terminals obtained from the first stage So we can get As follows,

[0135]

[0136] Further, we can get

[0137] If we want to recover the channel matrix H between the base station and the reconfigurable intelligent surface R,B We need to construct H R,B Decoupled atom set, as follows,

[0138]

[0139] So we can build an equivalent SDP optimization model, and the reason is as follows,

[0140]

[0141] So we can further write as follows,

[0142]

[0143] Where κ N Is a regularization parameter, generally set to By solving the above formula, we can get the top matrix And And the channel matrix We can get the reflection angle of the reconfigurable intelligent surface And the receiving angle of the base station By solving And The solution algorithm can be Root-MUSIC or ESPRIT algorithm; at this time, the path loss between the reconfigurable intelligent surface and the base station is obtained As follows,

[0144]

[0145] 4. Further, in step S3, after obtaining the channel parameters in step S2, the optimal phase control matrix of the reconfigurable intelligent surface for a single user can be obtained by using the incident angle information and the reflection angle information of the reconfigurable intelligent surface, specifically, S31, in the case of considering the known incident angle and reflection angle of the reconfigurable intelligent surface, the design of the phase control matrix of the reconfigurable intelligent surface becomes more convenient. Compared with other methods, this research does not need to solve the complex phase control matrix optimization function. For the kth user, we can use a simplified process to obtain the optimal phase control matrix Ω * .

[0146]

[0147] 5. Further, in step S4, after obtaining the two sub-channel matrices and the phase control matrix in step S3, we can combine them to construct the channel matrix of the user through the intelligent super surface to the base station, and then according to the obtained path gain, we can obtain the three-dimensional coordinates of the user and the base station with the reconfigurable intelligent surface as the origin, and then we can obtain the relative position of the user and the base station, specifically,

[0148] S41, for distance estimation, we consider the single slope model of the path loss and distance function, and the model formula can be expressed as follows,

[0149]

[0150] where P r represents the received power, P t represents the transmitted power, K is a constant coefficient dependent on the antenna characteristics and the average channel loss, which is generally set to d r is the reference distance of the antenna, which is usually assumed to be d r = 1m, is the actual distance, is the path loss exponent, which is usually assumed to be

[0151] Therefore, the path loss can be expressed as,

[0152]

[0153] Then [ρ M,R ]k and [γ R,B ] k Substituting into the above formula, the distance between the respective transmitting end and receiving end can be obtained respectively After successfully estimating the distance between the user and the reconfigurable intelligent surface and the distance between the reconfigurable intelligent surface and the base station, combined with the previously calculated incident angle and reflection angle of the reconfigurable intelligent surface, we can use the distance and angle information to deduce the relative positions of the base station, the reconfigurable intelligent surface and the user in the three-dimensional coordinate system by using the geometric relationship. Thus, the base station knows the position of the user and the distance between them.

[0154] The simulation experiment verification of the channel estimation and positioning in the scene based on the hybrid reconfigurable intelligent surface of the embodiment is as follows.

[0155] Simulation example: we choose N B =N M =12, N R =36, the number of users is set to K=3, all receiving angles and leaving angles are randomly and uniformly located in [0, π] and the interval between each angle is greater than the minimum angle interval required by the atomic norm, the path loss can be set to any real number in (0, 1), and the signal-to-noise ratio is defined as SNR=10log 10 (1 / σ 2 ). In addition, in the non-position-aware scene, we set the number of radio frequency chains at the reconfigurable intelligent surface N RF =6, we consider to do 100 independent experiments for the average, without loss of generality, when evaluating the effective SE boundary, we fix the channel coherence time to 2000 symbol periods. In order to further evaluate the performance of the proposed algorithm, this study will show the minimum mean square error results of channel parameters H M,R and H R,B . In the simulation verification of the non-position-aware scene, we set the total pilot signal occupancy T t =300. Considering that the number of radio frequency links is N RF =6, we can infer that in the first stage of this non-position-aware scene, the occupancy of the pilot signal is equivalent to 50 fast shots, and in the second stage, the occupancy of the pilot signal actually reaches 300 fast shots. The performance comparison of the embodiment method and the existing orthogonal basis matching algorithm is as Figure 6 , Figure 7 and Figure 8The figure shows the estimation error versus SNR, where the vertical axis represents the estimation error and the horizontal axis represents the SNR. It can be seen from the figure that the embodiment method has better performance than the prior art method. Although the present application has been described in detail with reference to the foregoing embodiments, modifications can be made to the technical solutions described in the foregoing embodiments, or some of the technical features can be replaced by equivalent features, and any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A channel estimation and localization method based on reconfigurable smart surface assistance under non-position-aware conditions, characterized in that: Includes the following steps, S1. Based on the Saleh-Valenzuela channel model, a channel model for the user to the base station through the smart metasurface is constructed. Utilizing the baseband processing capability of the hybrid reconfigurable smart surface, the channel model for the user to the base station through the smart metasurface is decomposed into two sub-channel estimation problems: the sub-channel between the user and the reconfigurable smart surface and the sub-channel between the reconfigurable smart surface and the base station. S2. The problem of solving the channel matrix of the two sub-channels is transformed into the problem of minimizing the atomic norm. Then, the decoupled atomic norm method is used to solve the channel parameters to reduce the amount of computation. S3. After obtaining the channel parameters, the optimal phase control matrix of the reconfigurable smart surface for a single user is obtained by using the incident angle information and reflection angle information of the reconfigurable smart surface. S4. After obtaining the two sub-channel matrices and the phase control matrix, they can be combined to construct the channel matrix from the user to the base station through the smart metasurface. Then, based on the obtained path gain, it is substituted into the single slope model to obtain the three-dimensional coordinates of the user and the base station with the reconfigurable smart surface as the origin, and then the relative position of the user and the base station can be obtained.

2. The channel estimation and localization method based on reconfigurable intelligent surface assistance under non-position awareness as described in claim 1, characterized in that: In step S1, based on the Saleh-Valenzuela channel model, a channel model for the user to the base station via the smart metasurface is constructed. Utilizing the baseband processing capabilities of the hybrid reconfigurable smart surface, the channel model is decomposed into two sub-channel estimation problems: the sub-channel between the user and the reconfigurable smart surface, and the sub-channel between the reconfigurable smart surface and the base station. Specifically, S11. A hybrid reconfigurable smart surface-assisted multiple-input multiple-output system, comprising a base station, a reconfigurable smart surface, and multiple users, wherein the base station and users are each configured with N array elements. B and N M A uniform linear array, while a reconfigurable smart surface is configured with N array elements. R The array is a uniform array, and the spacing between the array elements is half a wavelength; it is assumed that there is a control link between the reconfigurable smart surface and the base station, and that the direct path between the user and the base station does not exist due to obstruction; S12. When performing channel modeling, the SV channel model is used to describe the channel characteristics between the mobile user and the reconfigurable smart surface. This model uses the angle of arrival, departure angle, and corresponding path loss as basic parameters. Assuming only the direct path is considered, its corresponding delay is zero, and the path gain can be simplified to a real number. The expression for the channel model between the mobile user and the reconfigurable smart surface can be derived as follows: Where [θ M,R ] k This represents the emission angle of the k-th user. and Let ρ represent the azimuth and elevation angles incident on the reconfigurable smart surface for the k-th user, respectively. M,R ] k This represents the path loss of the k-th user's direct path, where K represents the total number of users, [H M,R ] k Let represent the channel matrix between the k-th user and the reconfigurable smart surface; for a uniform linear array with an element spacing of half a wavelength λ / 2, its array response is: in l represents the number of elements in the uniform linear array, so we have It is the array response vector at the k-th user, and For a uniform planar array with an element spacing of half a wavelength, its array response is: Where N x N represents the number of elements in a uniform area array located in the xoy plane along the x-axis. y Let represent the number of elements in the uniform area array along the y-axis, therefore we have It is the array response vector received at the reconfigurable smart surface from the k-th user, and S13. Similarly, the channel between the reconfigurable smart surface and the base station can be obtained as follows: Where υ R,B Indicates the receiving angle at the base station. and γ represents the azimuth and elevation angles of the reflection at the reconfigurable smart surface, respectively. R,B This represents the path loss of the direct path between the reconfigurable smart surface and the base station, and and The definition is the same as the definition in the previous formula. and The definition is the same as in the previous equation. Therefore, using the above equation and considering the reconfigurable smart surface, the total channel matrix is... for, in Let Ω be the phase control matrix of the reconfigurable smart surface. Here, it is assumed that the reconfigurable smart surface consists of a series of discrete phase controllers, i.e., Ω = diag(ω), where... and a∈[0,1], where it is assumed that the reconfigurable smart surface is a perfect reflective surface, that is, let a=1.

3. The channel estimation and localization method based on reconfigurable intelligent surface assistance under non-position awareness as described in claim 1, characterized in that: Furthermore, in step S2, utilizing the architecture of step S1, the problem of solving the channel matrix of the two sub-channels is transformed into an atomic norm minimization problem. Then, a decoupled atomic norm method is used to solve for each channel parameter to reduce the computational load. Specifically, S21. For uplink pilot training channel estimation, the user's N... M The pilot training sequence sent by the array element to the reconfigurable smart surface in the b-th time slot is: b∈{1,2,...,B}, and [S b ] :,1 =[S b ] :,2 =···=[S b ] :,T The phase control vector of the reconfigurable smart surface in the b-th time slot is used It means, and At the t-th snapshot within the b-th time slot, t∈{1,2,...,T}, M, which serves as the receiving signal in the reconfigurable smart surface. A Each element belongs to the index set. like Then the reconfigurable smart surface phase control matrix at the t-th snapshot within the b-th time slot is in this index set. The phase on is [Ω b ] i,i =0, in When, let N be set here. R =M A ×T, at this point, only M needs to be purchased for each piece. A If the position of each receiving element is chosen appropriately, then after T snapshots, T M elements can be... A The data from the single-digit snapshot are concatenated end-to-end to obtain an N. R Single snapshot data of dimension F = [E1, E2, ..., E T ] T ,in This N R The order of single-shot data in a given dimension is compared to that of N elements in a reconfigurable smart surface array. R The sequence of single-shot data in a dimension may be disordered, thus the data in the t-th time slot of the b-th time slot will be out of order. for X bt =Ξ t H M,R [S b ] :,t +N bt in Each column of this matrix contains at most one element that is 1, and all other elements are zero. The number of elements that are 1 in this matrix is ​​M. A indivual; Let represent independent and identically distributed additive white Gaussian noise, and let CN(0,σ) be the expression. 2 ), where σ 2 Represents the variance of the noise; T M A By concatenating the first and last data points of a single snapshot, we obtain an N. R Dimensional single-shot data Therefore, the received signal at the reconfigurable smart surface in the b-th time slot is represented as follows. in in The matrix contains only one element of value 1 in each row and column, with all other elements being zero, and the number of elements of value 1 in the matrix is ​​M. A ×T=N R Ξ is an identity array if and only if the receiving array elements of the reconfigurable smart surface are sequentially selected; Represents T M A A new N is formed by concatenating independent and identically distributed additive white Gaussian noise in dimension N. R Gaussian white noise of dimension N, and because each N bt All obey CN(0,σ) 2 Therefore, N b Still obeys CN(0,σ) 2 ),make Therefore, the received signals of all B time slots at the reconfigurable smart surface in the first stage are... as follows, S22. For the received signal at the base station, the received data at the t-th snapshot in the b-th time slot. as follows, in [Ω] b ] i,i =0, when hour; Let represent independent and identically distributed additive white Gaussian noise, and let CN(0,σ) be the expression. 2 ), where σ 2 Let the variance of the noise be denoted by , and then let . Obtain the received signal when the base station is in the b-th time slot. as follows, Y b =H R,B U b +Z b At this time, Therefore, the received signals at the base station in the second stage total B time slots. as follows, Y Sec =H R,B U+Z S23. In the first stage, to restore the channel matrix H between the user and the reconfigurable smart surface M,R First, construct H M,R The decoupled set of atoms is as follows. Therefore, an equivalent semidefinite programming (SDP) optimization model is constructed. Due to the non-convexity of rank calculation, the following equation is a trace minimization problem obtained by substituting the trace for the rank, which is the convex relaxation method mentioned earlier, where atoms... Norm convex relaxation to atoms Norms, as follows: Therefore, it can be further written as the following optimization problem. Among them κ M This is a regularization parameter used to balance signal sparsity and data fidelity. Under the assumption of independent and identically distributed Gaussian noise, this parameter is set to... Solving the above equation yields the Toplitz matrix. and and channel matrix Through the and The receiving angles of the reconfigurable smart surface are obtained by solving the problem. and the emission angle on the user side The solution algorithm is either Root-MUSIC or ESPRIT; however, after obtaining the receive angles of the K reconfigurable smart surfaces and the transmit angles of the K user sides, the correspondence between the receive and transmit angles is lost. This creates an obstacle to reconstructing the channel matrix between the reconfigurable smart surfaces and each user, and is also an unavoidable problem after decoupling. To solve this problem, firstly, H... M,R After vectorization, we have: Among them, vec(H) M,R All the bases are composed of Composed of K quantities 2 There are 1 basis, and the basis is orthogonal to each other. Construct all bases, to The objective function is defined using the OMP algorithm, which obtains the path loss of each angle while establishing the correspondence between the receive angle and the transmit angle. After obtaining the correspondence between the reception angle, transmission angle, and path loss, the channel matrix between each user and the reconfigurable smart surface is reconstructed. The reconstructed channel matrix of the k-th user is as follows. S24. In the second stage, the channel matrix H between the base station and the reconfigurable smart surface is first recovered using the received signal at the base station. R,B Then, the reconfigurable smart surface obtained from the first stage and the total channel matrix of all user terminals are utilized. Therefore, we obtain as follows, And thus obtain To recover the channel matrix H between the base station and the reconfigurable smart surface R,B H needs to be constructed first. R,B The decoupled set of atoms is as follows. Therefore, an equivalent SDP optimization model can be constructed, similarly as follows: Therefore, it can be further written as the following optimization problem. Among them κ N This is a regularization parameter, typically set to... By solving the above equation, the Toplitz matrix is ​​obtained. and and channel matrix Through the and The reflection angles of the reconfigurable smart surface are obtained by solving the problem. and the receiving angle of the base station The solution algorithm is either the Root-MUSIC or ESPRIT algorithm; in this case, the path loss between the reconfigurable smart surface and the base station needs to be obtained. as follows, 4. The channel estimation and localization method based on reconfigurable intelligent surface assistance under non-position awareness as described in claim 1, characterized in that: Further, in step S3, after obtaining the channel parameters in step S2, the optimal phase control matrix of the reconfigurable smart surface for a single user is obtained through the incident angle information and reflection angle information of the reconfigurable smart surface. Specifically, S31. Given the incident and reflection angles of the reconfigurable smart surface, for the k-th user, the optimal phase control matrix Ω can be obtained using a simplified process. * ; 5. The channel estimation and localization method based on reconfigurable intelligent surface assistance under non-position awareness as described in claim 1, characterized in that: Furthermore, in step S4, after using the two sub-channel matrices and phase control matrix obtained in step S3, they can be combined to construct the channel matrix from the user to the base station through the smart metasurface. Substituting the obtained path gain into the single-slope model, the three-dimensional coordinates of the user and the base station with the reconfigurable smart surface as the origin are obtained, and thus the relative positions of the user and the base station are calculated. Specifically, S41. For distance estimation, a single-slope model of path loss versus distance function is adopted, and its model formula is expressed as follows. Where P r P represents the received power. t This represents the transmit power, where K is a constant coefficient dependent on antenna characteristics and average channel loss, typically set to... d r This is the reference distance for the antenna, usually assumed to be d. r =1m, This is the actual distance. It is the path loss exponent, which is usually assumed to propagate in free space. Therefore, the path loss is expressed as, Then the solution (1-[ρ M,R ] k ) and (1-[γ R,B ] k Substituting these values ​​into the above formula, we can obtain the distances between the respective transmitters and receivers. After successfully estimating the distance between the user and the reconfigurable smart surface, as well as the distance between the reconfigurable smart surface and the base station, the relative positions of the base station, the reconfigurable smart surface, and the user in the three-dimensional coordinate system are derived using geometric relationships based on the previously calculated incident and reflection angles of the reconfigurable smart surface and these distance and angle information. This allows the base station to know the location of the user and the distance between them.

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